Question

if one root of the equation 4x^2-2x+(lambda -4)=0 is reciprocal of the other ,then find the value of lambda​

Answer 1

Answer:

λ = 4

Step-by-step explanation:

4$x^{2}$ - 2$x$ + (λ - 4) = 0

On comparing with a$x^{2}$ + b$x$ + c = 0,

        a = 4, b = -2, c = λ - 4

Let α, 1/α be roots of the equation (given that roots are reciprocal to each other)

We know that product of roots in a quadratic polynomial = c/a

⇒ α x 1/α = (λ - 4)/4

⇒ 1 = (λ - 4)/4

⇒ 4 = λ - 4

⇒ λ - 4 = 4

⇒ λ = 4 + 4

⇒ λ = 8

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